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Author ORCID Identifier
https://orcid.org/0000-0001-6861-4242
AccessType
Open Access Dissertation
Document Type
dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Mathematics
Year Degree Awarded
2020
Month Degree Awarded
February
First Advisor
Paul Hacking
Subject Categories
Algebraic Geometry
Abstract
In this thesis we identify certain cluster varieties with the complement of a union of closures of hypertori in a toric variety. We prove the existence of a compactification $Z$ of the Fock--Goncharov $\mathcal{X}$-cluster variety for a root system $\Phi$ satisfying some conditions, and study the geometric properties of $Z$. We give a relation of the cluster variety to the toric variety for the fan of Weyl chambers and use a modular interpretation of $X(A_n)$ to give another compactification of the $\mathcal{X}$-cluster variety for the root system $A_n$.
DOI
https://doi.org/10.7275/15991744
Recommended Citation
XIE, FEIFEI, "COMPACTIFICATIONS OF CLUSTER VARIETIES ASSOCIATED TO ROOT SYSTEMS" (2020). Doctoral Dissertations. 1871.
https://doi.org/10.7275/15991744
https://scholarworks.umass.edu/dissertations_2/1871